Inverse Anderson transition caused by flatbands

We propose a new disorder-induced insulator-metal transition of one-electron states, which may be called the "inverse Anderson transition." We first make a highly degenerated localized states by constructing a three-dimensional periodic system possessing only flat dispersion relations. When we introduce a disorder into it, a finite-size scaling of the level statistics shows two clear (localization-delocalization and delocalization-localization) transitions for a wide range of the energy, with increasing the degree of disorder. These transitions are confirmed also by finding the system-size-independent characteristic of the wave function.